A current measurement system generally must measure a very wide range of current levels. For example in an automotive battery system, the net current supplied from the battery can range from hundreds or thousands of amperes when the engine is being started, to tens of milliamperes when the car is off. To accurately determine the state of the battery capacity, it is necessary to measure this current as accurately as possible. The current from the battery is generally first converted to a voltage, for example by placing a small valued resistor in series with the current flow, and this voltage is then converted to a digital form using an analog to digital converter (ADC). The voltage signal is generally first amplified with a programmable-gain-amplifier (PGA), so that when the current is of a low level the voltage signal is gained up by a large gain to make use of the full dynamic-range of the ADC. In addition, to perform high accuracy measurements of the small voltages produced from low currents, it is generally necessary to perform the analog to digital conversion at a relatively slow rate, minimizing the effects of noise in the measured signal and in the measurement system. The decision of what level of amplification and conversion speed to use is generally determined by a processor, based on previous ADC results. Because of the slow conversion rate when the current is low, a sudden increase in the current drawn from the battery may take a relatively long time to be reflected in the ADC conversion result. This is potentially a problem for measuring the state of the battery, because calculations to determine the capacity of the battery require high-speed measurements that start as soon as possible after large currents are drawn. Therefore it would be advantageous if a current measurement system could perform high-accuracy measurements when the current is at a low level, while simultaneously being able to rapidly react to a large increase in current. U.S. Pat. No. 5,777,911 describes a Digital Filtering System incorporating a selector section, for producing an output signal from either a relatively narrow or low frequency width filter or a relatively wide or high frequency width filter selectively in accordance with the time rate of change in the level of the input signal fed to the filtering system. This filtering system could potentially be used following an ADC in a current measurement system. However, this scheme relies on the input signal being always within the range of the digital filtering system, and, implicitly, the input signal to the ADC always being within the range of the ADC. The current measurement system generally requires the use of a high-gain amplifier preceding the ADC when the current is of a low-level. Therefore following a sudden increase in current the amplified input to the ADC will generally be outside the range of the ADC, and any results produced from the ADC will generally be clamped to +full-scale or −full-scale. Even if the digital filtering system switches to the wide-bandwidth filter the results are still in error because the input to the filtering system is over ranged.